Question: Given $ m \angle MON = 6x + 124$, and $ m \angle LOM = 4x + 26$, find $m\angle LOM$. $O$ $L$ $N$ $M$
From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {4x + 26} + {6x + 124} = {180}$ Combine like terms: $ 10x + 150 = 180$ Subtract $150$ from both sides: $ 10x = 30$ Divide both sides by $10$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 4({3}) + 26$ Simplify: $ {m\angle LOM = 12 + 26}$ So ${m\angle LOM = 38}$.